Back to Newtonian Time?
| Scientific Paper | |
|---|---|
| Title | Back to Newtonian Time? |
| Read in full | Link to paper |
| Author(s) | Thomas E Phipps |
| Keywords | Relativity, Inertial Transformation, Neo-Hertzian Electromagnetism, Proper Time, Collective Time, GPS Time, Newtonian Time, Invariance, Covariance |
| Published | 2009 |
| Journal | Physics Essays |
| Volume | 22 |
| Number | 2 |
| No. of pages | 20 |
| Pages | 124-134 |
Read the full paper here
Abstract
An alternative approach to relativistic physics is reviewed, based on an invariant formulation of electromagnetic field theory due to Hertz. Both electromagnetism and mechanics are shown to be subject to reformulation whereby true invariance replaces "universal covariance." The invariant feature of Einstein's theory, proper time, is retained, but is supplemented for convenience in describing many-body motions by a generalized form of frame time termed "collective time" (CT), patterned on Global Positioning System (GPS) time. CT resembles Newton's absolute time in regard to environmental independence, but is shown to satisfy a form of relativity principle. A crucial experiment is described involving accurate measurement of stellar aberration at second order by means of the Very Long-Based Interferometry (VLBI) system. This would decide definitively between the Hertz and Maxwell-Einstein formulations of electromagnetism. Another experiment that I proposed earlier,3 involving in-orbit light speed measurement, is disavowed, since I now recognize it as not crucial. This paper sums up a half-century of my dissident thinking in physics and forms a concluding testament.
Overview
Thomas E. Phipps, Jr. describes this Physics Essays paper as his "concluding testament" — the summing-up of a half-century of dissident work. Its thesis is that the choice made by physics around 1905 was not forced by experiment but by an unwillingness to touch Maxwell's equations. Because those equations are not invariant under the Galilean transformation, Einstein and Lorentz kept them intact and instead altered the description of inertial motion, adopting the Lorentz Transformation and a weakened notion of form preservation called covariance. Phipps argues that Heinrich Hertz had already published, before 1894, an electromagnetism that is genuinely invariant under the Galilean transformation, and that it is a formal covering theory of Maxwell's — reducing to Maxwell's identically in a limiting case.
The departure from the standard account is sharp but selective. Phipps keeps proper time dτ, which he regards as the only part of special relativity that "correlates directly with reality", and rejects the companion spacelike interval dσ and everything built on it, including Length Contraction and Minkowski spacetime. He then rehabilitates frame time under a new name, collective time, modelled explicitly on the way GPS clocks are rate-adjusted, and argues that this restores to physics the practical virtues of Newton's absolute time — environmental independence and workable distant Simultaneity — without violating a relativity principle. The paper's operative content is a single proposed decisive test: a second-order measurement of Stellar Aberration by VLBI.
The argument
What went wrong at first order
Phipps opens with a methodological warning: "Science-by-consensus affords no protection against error-by-consensus", and there is nobody in the profession whose job it is to look for systematic error. Axioms, he adds memorably, "do not banish error – they provide it a respectable up-town dwelling place behind a manicured front lawn."
His technical complaint begins with the time equation of the Lorentz transformation, t ' = γ(t − vx/c2), which at first order in v/c reduces to t ' = t − vx/c2. This first-order alteration of Newtonian t ' = t, he insists, is never challenged and has no empirical support. Worse, he argues, it should have visible consequences: at times of order t ~ vx/c2 (femtoseconds) atomic resonant oscillations ought to show phase shifts over laboratory distances, and at distances x ~ c2t/v of a few thousand light years astronomical sources ought to show optical phase shifts of annual period tracking Earth's orbit. Neither is reported. "No known physical facts speak for the LT as a descriptor of inertial motion."
Invariance versus covariance
Phipps formalizes the distinction he thinks was fudged. An expression is invariant if the transformation preserves the symbols and their relationships with no nontrivial change of symbol definition — Newton's second law under the Galilean transformation is his example. It is covariant if the relationships are preserved but the symbols are redefined, as Maxwell's field components are recombined linearly under the Lorentz transformation. "Covariance is a looser expression of the form preservation idea than invariance," and traditionally it is the invariant that correlates with the real. He attributes the profession's acceptance of covariance to aesthetics — "Elegance is the mathematician's Lorelei" — and to the relief of not having to think a new thought about electromagnetism.
Hertz's operator, and a new reading of it
The Hertzian cure is formally slight: replace the non-invariant partial derivative ∂/∂t everywhere in the field equations by the total derivative
- d/dt = ∂/∂t + vd · ∇
which is Galilean invariant, since vd' = vd − v cancels the term picked up by ∂/∂t. Setting vd = 0 recovers Maxwell exactly, which is why Phipps calls Hertz's theory a covering theory.
Hertz's error, on this account, was interpretive, not formal: he read vd as an ether wind, "the trendy thing of his day", which led to disagreement with observation and the theory was dropped. Phipps's repair is to define vd as the velocity of the field detector relative to a fiducial inertial state. This turns the whole dispute into one about a parametric omission: Maxwell's equations parameterize source motion through the current js but say nothing at all about sink (detector) motion — a strange gap in a theory claiming source–sink reciprocity, and stranger still given that quantum theory makes detection the crux of what is physically real. He presses the point in the one-photon limit: Maxwellian covariance requires each inertial observer to have his own detector at rest at his own field point, but only one detector can register a single field quantum and the others must read zero, so the Lorentz relations among their readings cannot be satisfied. In the Hertzian scheme there is one detector viewed by many observers, each with his own value of vd, and numerical invariance (E ' = E, B ' = B) is trivial.
Neo-Hertzian equations
Replacing Newton's t in Hertz's equations by the invariant proper time τ gives the "neo-Hertzian" vacuum field equations, e.g.
- ∇ × B − (1/c) dE/dτ = (4π/c) jm, ∇ × E = −(1/c) dB/dτ, ∇ · B = 0, ∇ · E = 4πρ
with jm = js − ρvd to account for detector convection, and d/dτ = γ(∂/∂t + Vd · ∇). Galilean form invariance requires one further postulate, stated flatly: object length is a physical invariant. The same substitution of τ for t in mechanics gives F = dp/dτ, which reduces in laboratory time to Flab = d(m0γ dr/dt)/dt — the relation Phipps concedes is "probably the empirically best-confirmed prediction of special relativity theory", and which he stresses validates dτ invariance only, never dσ. He notes the parallel operator substitutions carrying the scheme into quantum mechanics and Dirac's electron equation.
His rejection of dσ is uncompromising: it has no operational definition, and since dσ = ic dτ is imaginary when dτ is real, it is "unsuited to describe physical reality". All "world-structural" claims of relativity resting on it are declared spurious.
Collective time
Proper time has practical defects: it belongs to one body only, so it is poorly suited to many-body problems, and dτ is inexact so τ cannot serve as a geometrical coordinate. But dt = γ dτ is a Pfaffian form in which γ is an integrating factor rendering dt exact. Phipps's model for the resulting "collective time" is the GPS: its clocks are rate-adjusted before launch so that all run in step regardless of motion and gravitational potential, which makes them "emphatically not Einstein clocks". Generalizing, CT is a space-filling set of arbitrarily-moving clocks all corrected to a single fiducial Master Clock in some inertial state; Einstein frame time is the special case where all clocks co-move. Because the natural rates of two Master Clocks in relative motion differ by a constant α, and t ' = αt merely rescales force units, Phipps invokes Newton's Principle of Similitude to argue that a relativity principle still holds: "the laws of nature are invariant under changes of inertial reference system." Since CT is divorced from any spatial frame, he takes this to expose "the foolishness of 'spacetime'", space and time "having nothing inherently to do with each other."
On a hyperplane of constant CT he then permits instantaneous action at a distance, restoring Newton's third law in its full form (equality, simultaneity and collinearity of distant action–reaction) and, he claims, dissolving the conflict between quantum non-locality and field theory. Retardation at speed c applies to radiation, he argues, not to forces; he cites Laplace's argument that a gravity propagating at c would disrupt the solar system within a couple of hundred million years.
Light speed, and the crucial experiment
The neo-Hertzian wave equation ∇2E − (1/c2) d2E/dτ2 = 0 has phase speed ±c + Vd·k/k. The first-order term is dismissed as unobservable by Potier's Principle — it plays formally the same role as an ether wind, which nineteenth-century analysis showed produces no interferometric effect. What remains, measured against collective time, is
- u = √(c2 − v2) = c/γd
so a moving detector measures a genuinely slowed light speed — but only with a CT clock. A proper-time clock always measures c, in agreement with Einstein's second postulate, because it runs γd times slower. Phipps explicitly retracts his own earlier prediction about an orbiting dual-function clock ("Mea culpa"), having overlooked this physical slowing; the corrected prediction is that in orbit the τ-clock reads c and the CT clock reads c/γd. On this reading, the constancy of light speed is not a postulate but "an artifact of speed measurement with clocks uncorrected for environmental influences."
The decisive test is stellar aberration at second order. Special relativity predicts an aberration angle whose expansion contains a non-zero second-order term in (v/c)2, largest when the star lies 45° from the ecliptic and Earth moves toward or away from it. The neo-Hertzian formula, written in terms of detector speed vd = vorb, lacks that term entirely. "Einstein's second-order term is predicted to be absent." VLBI resolution is, Phipps believes, adequate to look, and to his knowledge the measurement has never been made. He adds a subsidiary objection: the aberration parameter is empirically Earth's orbital speed, independent of source motion, which sits awkwardly with a four-vector treatment in which v should be source–sink relative velocity.
Assessment
The strongest thing about this paper is that it makes a prediction that could kill it, states it plainly, and identifies existing hardware capable of the measurement. That is rare in this literature, and Phipps knows it — he confesses this is "the only crucial experiment I have been able to find" in fifty years, and he is honest enough to observe that "often the most disparate theories can map onto much the same set of observations", so that boasting of theoretical success is "vainglorious". The historical point at the core is also correct and under-appreciated: Hertz did publish a Galilean-invariant electrodynamics; it is a formal covering theory of Maxwell's in the sense claimed; and it was abandoned largely because of its ether-wind interpretation rather than any defect of the formalism. Reinterpreting Hertz's velocity parameter as detector velocity is a genuinely original move, and the observation that Maxwell's equations parameterize source motion but not sink motion is a real asymmetry in a theory that advertises reciprocity. The self-correction of his own earlier orbiting-clock prediction is a mark of seriousness.
The difficulties begin with the paper's central rhetorical claim, that the Lorentz transformation lacks empirical support at first order. The two null results Phipps offers are asserted, not calculated: no derivation is given showing that the relativity of simultaneity should produce femtosecond phase shifts over laboratory distances or annual optical phase shifts from sources thousands of light years away, and neither argument confronts the fact that the vx/c2 term concerns the labelling of distant events, not the phase of a locally detected wave. Against this stand direct measurements he does not address: the Kennedy–Thorndike experiment, the Ives–Stilwell transverse Doppler measurement, and the flight and satellite comparisons of atomic clocks all constrain precisely the combination of rate and simultaneity effects at issue. His rejection of length contraction as having "not a shred of empirical evidence" is stated rather than argued, and it becomes a postulate of length invariance on which the Galilean invariance of his own field equations depends — so the theory's viability rests on the very claim most in dispute, asserted rather than derived.
Several other steps are asserted. The mathematical argument that dσ cannot be real because ic dτ is imaginary is a statement about a sign convention, not about physics; the same reasoning would disqualify any spacelike separation, including the ordinary distance between two simultaneous events. The move from proper time to collective time is presented as a discovery about time when it is, by his own description, a choice of units and clock corrections — he concedes "there is obviously nothing 'absolute' about physical time", which considerably weakens the paper's title question. The instantaneous action-at-a-distance on the CT hyperplane is admitted to have "no empirical evidence to confirm or disconfirm it", and the Laplace argument for infinite-speed gravity is now understood to be an artefact of treating gravity as a simple central force: the velocity-dependent terms of general relativity cancel the aberration to very high order, and binary pulsar orbital decay (PSR B1913+16) measures gravitational radiation at the general-relativistic rate to better than a percent, which requires finite propagation speed. That measurement postdates none of the paper's argument and is not mentioned.
The crucial experiment itself carries a caveat Phipps does not examine: the second-order aberration term in question is of order (vorb/c)2 ≈ 10−8 in angle, and disentangling it in VLBI data requires the full modelled chain of Earth orientation, troposphere and gravitational deflection — all of which are currently reduced using relativistic models. A null result would therefore be difficult to interpret as cleanly as the paper suggests. Nor does Phipps show his aberration formula (27) reproduces the well-measured first-order Bradley constant with the same rigour he demands of others; it is quoted from earlier work.
Finally, the tone will cost the argument readers it might otherwise have. Phrases such as "the holy consensus", "Immaculate Conception", and the invitation to the "orthodox reader to deploy his own defenses of his indefensible belief" are not arguments, and they sit oddly beside the paper's own plea that a new paradigm not be judged by the presuppositions of the old. Judged on its physics rather than its manner, this is a carefully built alternative formalism that agrees with Einstein wherever measurement is good, differs where measurement is absent, and asks for one specific observation. That is a defensible position to end a career on; it is not yet a demonstration.